The present invention relates generally to model predictive control apparatus, and more particularly to model predictive control apparatus for automotive vehicles which predicts future dynamic behaviors of the host vehicle and target vehicles around the host vehicle, and optimizes a control input to the host vehicle in accordance with the prediction.
In recent years, there have been proposed and disclosed various model predictive control (MPC, or model-based predictive control (MPDC)) systems. In general, a model predictive control method is configured to predict a time series of a state of a system in accordance with a mathematical model of the system, to define an objective function to numerically evaluate the predicted time series system state and a future time series of a control input to force the system state to track its setpoint, to calculate an optimal value of a future time series of the control input which minimizes the objective function, and to input the calculated optimal value of the control input to the system.
A Published Japanese Patent Application No. H7(1995)-191709 (hereinafter referred to as “H7-191709”) shows a parameter setting method for the model predictive control. The method disclosed in H7-191709 is configured to check the condition numbers of matrices whose inverse matrices are calculated and used in its computational process, when parameters of a model predictive control system are changed, and to adjust a weight for a control input in an associated objective function so that the condition numbers are held within predetermined bounds. Incidentally, the condition number of a matrix A is the ratio of its maximum singular value to its minimum singular value. The condition number is a measure of the sensitivity of solution of Ax=b to perturbations of A or b (x and b are vectors). In other words, the condition number is a measure of the numerical accuracy of its inverse matrix A−1. In general, with increasing condition number of a matrix, the numerical accuracy of its inverse matrix decreases so that it becomes more difficult to accurately calculate its inverse matrix. Thus, the method disclosed in H7-191709 has intention to prevent the control input from violating its constraints due to computational errors or computational abnormality, monitoring the condition numbers of the matrices concerned. When there is a possibility that a large condition number adversely affects the control computation, the method increases the weights for the control input in the objective function to equivalently reduce the condition number, and to hold the stability of the control computation.
A Published Japanese Patent Application No. 2000-135934 shows an automatic vehicular velocity control apparatus for automotive vehicle, which has intention to follow up a preceding vehicle which is running ahead of the vehicle at an appropriate inter-vehicle distance when the preceding vehicle has been recognized. In addition, a reference “T. Ohtsuka, “Continuation/GMRES method for fast algorithm of nonlinear receding horizon control” Proc. 39th IEEE Conference on Decision and Control, pp. 766-771, 2000” shows an algorithm for model predictive control in which the control input to a system is updated by a differential equation to trace the solution of an associated two-point boundary-value problem.